Compactification
of the Bruhat-Tits Building of PGL
by Lattices of Smaller Rank

In this paper we construct a compactification of the Bruhat-Tits building
associated to the group $PGL(V)$ by attaching all the Bruhat-Tits buildings
of $PGL(W)$ for non-trivial subspaces $W$ of $V$ as a boundary.